Woodward has come under severe pressure over the way the club is being run and has been the subject of unsavoury chants by the supporters in recent games against Burnley and Tranmere Rovers.
In a video that has gone viral online, a group of supporters can be seen hurling flares into Woodward’s home.
It is understood that neither Woodward nor his wife and two daughters were at home when the incident took place.
A Cheshire Police statement read: "At around 10.45pm on Tuesday 28 January, Cheshire police were notified of an incident of criminal damage that had taken place earlier this evening with a large group targeting a property.
"Thankfully no-one was harmed, and officers will liaise with security officials over the coming days to establish the full circumstances surrounding this incident and identify those involved."
Manchester United are fifth in the Premier League and are in danger of missing out on Champions League football for a second straight season.
The Red Devils are 33 points behind leaders Liverpool and have so far made no signings in the January transfer window despite significant injuries to top scorer Marcus Rashford, Paul Pogba and Scott McTominay.
United are assisting police in investigations and have promised to hand lifetime bans to anyone found in connection to the attack.
The Old Trafford outfit released the following statement regarding the incident: "Manchester United Football Club have tonight been made aware of the incident outside the home of one of our employees.
"We know that the football world will unite behind us as we work with Greater Manchester Police to identify the perpetrators of this unwarranted attack.
"Anybody found guilty of a criminal offence, or found to be trespassing on this property, will be banned for life by The Club and may face prosecution.
"Fans expressing opinion is one thing; criminal damage and intent to endanger life is another. There is simply no excuse for this."
